How to solve
v(t) = s'(t): differentiate the position polynomial, then evaluate at the requested time.
Steps
- Differentiate s(t) term by term.
- Substitute the given t.
- Negative velocity means moving backward.
Example
s(t) = t³ − 6t². Find v(3).
- v(t) = 3t² − 12t.
- v(3) = 27 − 36 = −9.
Answer: -9
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